1. Field of the Invention
This invention relates to a superconducting weak link device which links two superconductors.
2. Prior Art Statement
The Josephson effect, a specialized tunnel effect in the superconducting state, was theoretically predicted by B. D. Josephson in 1962 and experimentally verified soon thereafter. The Josephson effect had been initially thought to be a superconductive tunneling phenomenon of electron pairs occurring at a so-called tunnel Josephson junction where two superconductors are separated by a thin insulating film. Thereafter, the same Josephson effect was observed in point contact junctions where two superconductors are in contact at a point as well as in bridge-type junctions as shown in FIG. 1 in which a narrow constriction (bridge) 2 is provided on a superconducting thin film 1, leading to the development of many variations in shape. To differentiate them from tunnel junctions, the point contact junctions and bridgetype junctions are called weak link junctions, and while the former's current-voltage characteristic exhibits a large degree of hysteresis between the zero voltage state and the energy gap voltage, the latter weak-link type junctions are characterized by a current-voltage characteristic free of hysteresis as shown in FIG. 2. With tunnel junctions which have a large degree of hysteresis, it is normally difficult to set them to a voltage in the finite voltage state of 0&lt;V&lt;2.DELTA./e using normal current-source biasing. In either case, a supercurrent flows in the zero-voltage state until the current flowing across the junction reaches a critical value and, in the nonzero-voltage state, current oscillation of a frequency proportional to the voltage, known as the ac Josephson effect, begin to occur, and if irradiated with electromagnetic waves, current steps will appear at equal voltage intervals on the current-voltage characteristic. These steps appear at voltage intervals of hf/2e which is the inverse of the Josephson frequency-voltage ratio 2e/h, a fixed unvarying fundamental constant, multiplied by the frequency f of the electromagnetic waves, where h is Planck's constant and e is the elementary electron charge. Since this step voltage can theoretically be obtained at the precision of the frequency f, this Josephson effect has found practical application in the voltage standard technology. Its sharp non-linear effect with respect to electromagnetic waves is also promising in applications to highly sensitive detection of electromagnetic waves, so research and development is proceeding continuously.
The phenomenon of electrons tunneling between the two superconductors across the barrier of the Josephson junction based on coupling of the wave functions of the electrons is understood to be caused by the wave nature of particles, but when the size of the junction becomes extremely small, the change in electrostatic energy e.sup.2 /2C accompanying tunneling of an electron or electron pair (or (2e).sup.2 /2C for the case of an electron pair) is known to affect the tunnel phenomenon.
Recently, a phenomenon which has attracted much interest in physics as a new quantum effect in solid-state device has been the quantization phenomenon of tunnel current in extremely small junctions. This phenomenon is one which occurs when the particle nature of the electron dominates the tunnel effect so that the change in the electrostatic energy due to the tunneling of one particle is much greater than the coupling energy of the junction device, electrostatically blocking the tunneling of other particles (an effect called the coulomb blockade). In junctions in which this coulomb blockade acts, single electron tunneling occurs regularly at a frequency of f =I/e, and when a very small tunnel-type Josephson junction is operated at a constant current at low temperature (T&gt;e.sup.2 /k.sub.B C, where k.sub.B is Boltzmann's constant) regular electron-pair tunneling occurs at a frequency of f=I/2e. This phenomenon, variously known as single-electron-tunneling, (SET) oscillation, Bloch wave oscillation, etc., is standards and new devices which function with one electron, along with studies of its potential in new applications.
The Hamiltonian H of a very small Josephson junction biased by a current source is represented by equation (1). ##EQU1##
The first term on the right side of this equation (1) is the electrostatic energy, where n is the relative number of electron pairs, given by n=N.sub.2 -N.sub.1.The second term on the right side is the Josephson coupling energy, where .theta. is the phase difference, given by .theta.=.PHI..sub.2 -.PHI..sub.1. The third term on the right side represents the interaction between the current I from the current source and the Josephson junction.
In Josephson junctions fabricated by typical thin-film microprocessing technology, the change in electrostatic energy 2e.sup.2 /C due to the tunneling of one electron pair is sufficiently small in comparison to the Josephson coupling energy E.sub.j that the first term in the right side of equation (1) is negligible and the normal Josephson effect is obtained.
This Josephson effect occurs in the bridge section 2 which connects the two superconductors 1 in FIG. 1, and in this case the length of the bridge section 2 is of particular importance. If this length is within the range of 1 to 5.31 times the coherence length of the superconductor, the current flowing within the bridge section will include a supercurrent I.sub.S, and this supercurrent will not depend on of the voltage across the junction, but rather depend on the phase difference .theta.=.PHI..sub.2 - .PHI..sub.1 between the phases .PHI..sub.1 and .PHI..sub.2 of the wave functions in the two superconductors. Since .differential.H/.differential..theta.=0 in the equilibrium state, from equation (1), the current I.sub.s (.theta.) is represented as in equation (2), EQU I.sub.s (.theta.)=I.sub.c sin.theta. (2)
where I.sub.c is the critical current, given by I.sub.c =2eE.sub.j .
The phase difference .theta. is related to the voltage V between the superconductors by equation (3), ##EQU2## where eV=.mu..sub.2 -.mu..sub.1 (.mu..sub.1 and .mu..sub.2 are the electrochemical potentials of the respective superconductors). When voltage V is nonzero, Josephson oscillation of the junction supercurrent occurs.
Thereby, if an ac voltage of frequency .OMEGA. overlaps with the dc voltage V across the two sides of the junction, the current will contain a Fourier component of frequency 2eV/h.+-.nf, where n is an integer. If the frequency is 2eV/h =nf for an integer n, the supercurrent will contain a dc component which depends on the phase of oscillation of the ac voltage. Hence, its dc characteristic will have a resistance portion of zero slope in the current region corresponding to the ac voltage oscillation, as in the current-voltage characteristic under irradiation of electromagnetic waves shown in FIG. 2.
Next, series connection of Josephson junctions will be described. In the case of a device in which M Josephson junctions of the same characteristics are connected in series, the junctions in the array must be considered to each have slightly different values for their junction resistance Rk and critical current I.sub.k (where k=1, 2, 3 . . . M). By using a current source of sufficiently high impedance in comparison to the device resistance to apply a dc bias to this device, the common dc current is determined by the current source, and a finite voltage V.sub.k is generated at a current greater than the critical current, causing an oscillating current of frequency f.sub.k =2eV.sub.k /h based on the ac Josephson effect, effectively creating a system of M oscillators connected in series as shown in FIG. 3(b). While these ac current components flow as a common current, from a dc point of view the finite voltage V.sub.k is determined by the current I and the junction resistance R.sub.k, so variation occurs between the frequencies f.sub.k-1, f.sub.k, f.sub.k+1 of adjacent junctions. If there is no fluctuation in the same junction parameters, the phase differences .theta..sub.1, .theta..sub.2 , . . . .theta..sub.M will be identical, but an array in which interaction between junctions are negligible would lack a means of recovery from external perturbation, so Josephson devices linked in series are usually considered to be independent of each other.
In a purely one-dimensional system, the probability of an order defect occurring somewhere increases linearly with number M of junctions connected in series, so fluctuations as a system diverge. However, all natural one-dimensional systems are commonly weakly interacting parallel-chains, and in fact the interaction between elements intervenes, so ultimately the dynamic process of the system as a whole greatly depends on the type and strength of the interactions through these chains.
When connecting a plurality of Josephson devices of the same junction characteristics in series, if some sort of synchronizing action due to high-frequency coupling is present, oscillations due to the ac Josephson effect in M weak links in series have been reported to exhibit superimposition at roughly the same phase. In this case, the ac voltage is amplified by a factor of M and the oscillation power amplified by a factor of M.sup.2. Here, the voltage V.sub.k across the junctions remains equal for a long period and perturbations are at low frequencies. Over short periods, the frequency f.sub.k of each junction is given by equation (4) and the frequencies f.sub.1, f.sub.2, . . . f.sub.M become equal. ##EQU3##
If the Josephson devices in such a coherent state are externally irradiated by microwaves of frequency f, constant-voltage steps will appear in the current-voltage characteristic at intervals of Mhf/2e volts as shown in FIG. 3(c). However, in this case, the oscillation of each device is superimposed on the others at the same phase, but the quantum processes of the M stages are each independent so the bias voltage appears amplified by a factor of M. This is differentiated from the electromagnetic wave response characteristic of the case of a single weak link as shown in FIG. 2.
In an experiment in the 100-115 GHz band using series Josephson junctions of niobium thin film developed for use in mixers, its behavior was observed to be completely different than that of the well-known coherent operation (FIG. 3(c)) of normal series junctions. The series array devices used in the experimental research comprised Josephson junctions with short superconducting bridges of a quasi-planar-type structure; the devices were given junction resistances of 20-100 .OMEGA. in an attempt to achieve impedance matching. In the experiment, these series array junctions were biased by a voltage source circuit of much lower impedance than the junction resistance and the voltage across the ends of the array was fixed to a set dc value. The series Josephson junction array was mounted inside a quarterly reduced-height waveguide of a WR10-standard waveguide to assure highfrequency coupling. When irradiated with millimeter waves at a frequency of .OMEGA./2.pi., as in FIG. 2, a current step response unrelated to the series number M was observed at voltage intervals of .OMEGA./2e as if the entire system was a single Josephson-junction device.
This is understood as if the pair tunneling was constrained by an action stronger than that in a coherent state, resulting in a plurality of quantum processes being interlocked in series and appearing as a single quantum process. The cause of this strong interaction within the array in this case is thought to be the synergetic effect among several factors including: that there is a strong synchronizing action of high-frequency current between the junctions due to high-frequency coupling, that the voltage across the two ends of the series array is fixed at voltage of the low-impedance dc voltage source and voltage fluctuations at low frequency is inhibited by the voltage-source biasing, and other factors.
This result can be interpreted to mean that through the strong interaction between M Josephson junctions, the quantum processes of the whole are synchronized so that an M-order multi-photon process occurs more efficiently than those of other orders. With the purpose of checking this effect in another experiment and to experimentally verify the ability of this phenomenon to be used effectively in a high-order harmonic mixer in the submillimeter wave range, high-frequency mixer experiments were carried out at different orders between .multidot.th and 9th order between microwave local signals at 5.6-12 GHz. At an order matching the number of series stages of M=11, a relative improvement of the signal-to-noise ratio of 5 dB was obtained, demonstrating the fundamental theory. (T. Matsui, B. Komiyama & H. Ohta, IEEE Trans. Magn., Vol. 25, 1072, 1989.)
A superconductor which makes the transition to superconducting at a high temperature (critical temperature T.sub.c) typically has a short coherence length .apprxeq. so when forming tunnel-type Josephson junctions, the state of the thin-film surface and the quality of the interface greatly affects the junction characteristics. In particular, when using thin films of high-temperature oxide superconductors, their coherence length .apprxeq. is short, being roughly the same size as the unit cell, so it is extremely difficult to create a good tunnel barrier with a thin insulating layer between superconductors.
In addition, in the case of weak-link types represented by the bridge type, in order to expect a substantially ideal Josephson effect, the length of the constriction (bridge) 2 must be shorter than 5.31 times the coherence length. Thus, when considering the process of forming various types of thin-film junctions, one encounters as many technical difficulties as in the case of the tunnel-type junction, since the qualities of the initial deposition layer of film, thin-film surface and boundaries all greatly affect the characteristics of the junctions.